Dataset Information

Signatures of optimal control in pairs of schooling zebrafish.

ABSTRACT: Animals moving in groups coordinate their motion to remain cohesive. A large amount of data and analysis of movement coordination has been obtained in several species, but we are lacking theoretical frameworks that can derive the form of coordination rules. Here, we examine whether optimal control theory can predict the rules underlying social interactions from first principles. We find that a control rule which is designed to minimize the time it would take a pair of schooling fish to form a cohesively moving unit correctly predicts the characteristics of social interactions in fish. Our methodology explains why social attraction is negatively modulated by self-motion velocity and positively modulated by partner motion velocity, and how the biomechanics of fish swimming can shape the form of social forces. Crucially, the values of all parameters in our model can be estimated from independent experiments that need not relate to measurement of social interactions. We test our theory by showing a good match with experimentally observed social interaction rules in zebrafish. In addition to providing a theoretical rationale for observed decision rules, we suggest that this framework opens new questions about tuning problems and learnability of collective behaviours.

SUBMITTER: Laan A

PROVIDER: S-EPMC5394674 | biostudies-literature | 2017 Apr

REPOSITORIES: biostudies-literature

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Signatures of optimal control in pairs of schooling zebrafish.

Laan Andress A Gil de Sagredo Raul R de Polavieja Gonzalo G GG

Proceedings. Biological sciences 20170401 1852

Animals moving in groups coordinate their motion to remain cohesive. A large amount of data and analysis of movement coordination has been obtained in several species, but we are lacking theoretical frameworks that can derive the form of coordination rules. Here, we examine whether optimal control theory can predict the rules underlying social interactions from first principles. We find that a control rule which is designed to minimize the time it would take a pair of schooling fish to form a co ...[more]

PMID: 28404782

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Project description:The Bertalanffy-Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p * m a - q * mb . The special case using the von Bertalanffy exponent-pair a = 2/3 and b = 1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). Fitting VBGF to size-at-age data requires the optimization of three model parameters (the constants p, q, and an initial value for the differential equation). For the general Bertalanffy-Pütter model, two more model parameters are optimized (the pair a < b of non-negative exponents). While this reduces bias in growth estimates, it increases model complexity and more advanced optimization methods are needed, such as the Nelder-Mead amoeba method, interior point methods, or simulated annealing. Is the improved performance worth these efforts? For the case, where the exponent b = 1 remains fixed, it is known that for most fish data any exponent a < 1 could be used to model growth without affecting the fit to the data significantly (when the other parameters were optimized). We hypothesized that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and we tested this conjecture for a data set (20,166 fish) about the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. To this end, we assessed the fit on a grid of 14,281 exponent-pairs (a, b) and identified the best fitting model curve on the boundary a = b of the grid (a = b = 0.686); it corresponds to the generalized Gompertz equation dm/dt = p * ma - q * ln(m) * ma . Using the Akaike information criterion for model selection, the answer to the conjecture was no: The von Bertalanffy exponent-pair model (but not the logistic model) remained parsimonious. However, the bias reduction attained by the optimal exponent-pair may be worth the tradeoff with complexity in some situations where predictive power is solely preferred. Therefore, we recommend the use of the Bertalanffy-Pütter model (and of its limit case, the generalized Gompertz model) in natural resources management (such as in fishery stock assessments), as it relies on careful quantitative assessments to recommend policies for sustainable resource usage.

Dataset Information

Signatures of optimal control in pairs of schooling zebrafish.

Publications

Signatures of optimal control in pairs of schooling zebrafish.

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